# How do you find the product of (5c^3d)/(c^4d)*(f^2d^3c)/(10cf^4)?

Mar 4, 2018

$= \frac{5 {d}^{3}}{2 c {f}^{2}}$

#### Explanation:

This is all one big term with number and variable factors.

• Cancel the numbers $\frac{\cancel{5} {c}^{3} d}{{c}^{4} d} \times \frac{{f}^{2} {d}^{3} c}{{\cancel{10}}^{2} c {f}^{4}}$

• Multiply the numerators and multiply the denominators by adding the indices of like bases to give one fraction:

$= \frac{5 {c}^{4} {d}^{4} {f}^{2}}{2 {c}^{5} {\mathrm{df}}^{4}}$

• Divide by subtracting the indices of like bases so that the indices are left positive. (Big - small)

$= \frac{5 {d}^{3}}{2 c {f}^{2}}$